A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 μF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

Solution

Given, a series LCR circuit.
Impedence , Z = 20Ω

Inductance, L = 1.5 H
Capacitance, C = 35 μF

When the frequency of the a.c. supply is equal to the natural frequency, then

Impedence is equal to resistance.

i.e.,

z = R and ϕ = 0 °

∴

z = 20 Ω

Then,

I_{v} = \frac{E_{v}}{Z} = \frac{200}{20} = 10 A

Hence, average power transferred

P = E_{v} I_{v} \cos 0 ° = 200 \times 10 \times 1 = 2000 watt .

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Electrostatic Potential And Capacitance

A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 μF is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

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